1. Superglasses and the nature of disorder-induced SI transition
Xiaoquan Yu
Advisor: Markus Mueller
2,12,2012

2. Outline Introduction of spin glasses and Anderson localization.
Superglasses- mean field phase diagram.
Hard core boson model on a Bethe lattice with large connectivity.
Finite dimension

3. Anderson localization

4. Mobility edge

5. Spin glasses
A spin glass is a magnet with random frustrated interactions.
Ferromagnetic and antiferromagnetic bonds are randomly distributed.
Spin glasses display many metastable structures.
Many pure states.
Gaussion in one pure state

6. Motivations
Glasses + quantum fluctuations- quantum glasses. Low temperature properties?
Glasses+ superfluid ? Can two orders coexit?
Motivated by some supersoild experiments: amorphous solids sustain more robust supersolidity.
Disorder may be a crucial element in understanding the supersolid systems

7. Superglasses
Model and method
Self consistent equations
Replica method

8. Phasediagram QMC Gingras et al., PRL (2010). Glassy SIT! Not BCS type!
Robust to on-site disorder
Exact result!

9. Properties of superglasses phase
Local order parameters are anticorrelated
Non-monotonicity behavior of superfluid order parameter

10. Motivation and back grounds: conception
Dirty superconductor.
Anderson’s theorem breaks down.
Localization of bosonic particles--- Bose glass.
Properties of Bosonic insulators.

11. Motivation and backgrounds: experiments
Activated transport near the SIT
D. Shahar, Z. Ovadyahu, PRB 46, (1992).
J. M. Valles et al., PRL 103, (2009)
Activated behavior!
Indicating the exitence a boson mobility edge !

12. Ioffe-Mezard’s proposal
M. V. Feigel'man, L. B. Ioffe, and M. Mezard, PRB (2010).  L. B. Ioffe and M. Mezard, PRL(2010).
Model and cavity mean field method
Cavity Hamiltonian of spin j j
Order parameter of conducting phase

13. SI transition Susceptibility Replica method Self-average quantity
Participation ratio
1-m

14. Mobility edge ??? Whether the pertubations relax? Matrix elements
Pertubations on the boundary
Fermi golden rule
Should be -1

15. Phase diagram gc g gc g Temperature Temperature Energy Energy
Ioffe – Mezard’s results
Expected scenario
 L. B. Ioffe and M. Mezard, PRL(2010).
Temperature
Temperature
Energy
Energy
Green and red line
meet at zero energy
Full localization, no mobility edge!
Discrete levels
Continue spectrum
Discrete levels
Superconductor
Superconductor gc g gc g

16. Comments
If the density of state is uniform , why one should expect there is a mobility edge? Indeed, there is no mobility edge in their model! So a mobility edge never appears? It appears in a Glassy insulator!

17. Phase diagram Superfluid emerges without closing mobility gap!
Continue spectrum
Discrete levels
Glassy SIT
Superfluid emerges without closing mobility gap!
May explain the puzzling feature (activated behavior)of transport in dirty SC films.

18. Thank you!